As others have said, 4 weeks is still early days. When did the anxiety start? Straight away?
You might also want to try magnesium for relaxation? That’s always recommended alongside HRT for sleep and calming effect? BetterYou magnesium spray is a great one to try as it won’t affect your digestive system. I am now trying one by Newson health with b vitamins. And obvious thing, if you drink coffee/tea, don’t stop it but cut it down.
If you do any yoga, worth getting up and do some really calming poses, I particularly like doing a standing forward bend for 3 to 5 minutes (bent knees and head resting on sofa) when I wake up during the night and can’t get back to sleep, really calming.
Hope it eases soon.